Blender VSE Driver deleted when strip is copied or duplicated
The driver is not copied as the f-curve would have to be copied and the devs don't like to duplicate f-curves (as that gets quite messy).

Instead simply hover over the driver value in the first strip, right click and select "copy driver".
Go to the same value in the copied strip and right click then select "paste driver".

Remember that to see drivers update in the VSE you must either hit play or the button labeled "Update Sequencer" in the VSE timeline.